 
Summary: DOI: 10.1007/s002080020400y
Math. Ann. (2003) MathematischeAnnalen
Young's inequality in traceclass operators
Mart´in Argerami · Douglas R. Farenick
Received: 20 December 2001 / Revised version: 11 July 2002 /
Published online: 10 February 2003 © SpringerVerlag 2003
Abstract. If a and b are traceclass operators, and if u is a partial isometry, then u  abu
1
1
p ap
+ 1
q bq
1, where · 1 denotes the norm in the trace class. The present paper characte
rises the cases of equality in this Young inequality, and the characterisation is examined in the
context of both the operator and the HilbertSchmidt forms of Young's inequality.
Mathematics Subject Classification (2000): 47A63, 15A60
1. Introduction
Building on the work by T. Ando [A], it was shown in [EFZ] that for each pair of
compact operators a and b, and for each p, q R+
for which 1/p + 1/q = 1,
